A New Algorithm of Interpolation Wavelet Construction Based on Scaling Function

Interpolation wavelets are used widely in discrete signal processing. However, in classical wavelet sampling theory, interpolation wavelets are constructed by using orthogonal wavelets. This leads up to difficulty in obtaining interpolation wavelets. By analyzing reconstruction filters associated with interpolation scaling functions, a new method is proposed to construct interpolation wavelets. Since this new algorithm can construct interpolation wavelets without knowing orthogonal wavelets, it improves greatly efficiency of interpolating wavelet construction. In the examples, our algorithm is applied to some typical multiresolution analyses, which validate effectiveness of our algorithm.

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